The computed tomography imaging spectrometer (CTIS) is a snapshot imaging spectrometer, excelling in dynamic detection tasks. It can capture two-dimensional spatial information and spectrally compressed information of a target within a single exposure time. However, traditional CTIS image reconstruction algorithms suffer from missing-cone problem, which reduces the accuracy of spectral reconstruction. In recent years, deep learning has been applied to CTIS spectral image reconstruction, significantly improving spectral reconstruction accuracy compared to traditional algorithms. However, due to the missing-cone problem, it is difficult to accurately recover the truth of spectral data cube in the real scene. Currently, most CTIS neural network reconstruction models are trained using simulated datasets of spectral data cubes and diffractive images. Because these data differ significantly from real data under actual application conditions, the established models may not be effectively applicable to real-world scenes. Therefore, we propose a new CTIS system based on slit-scanning architecture utilizing an adjustable slit aperture to obtain the real spectral data cube of the target while maintaining the simplicity of the CTIS structure. By limiting the field of view (FOV) through the slit, the area of diffraction overlap can be reduced, thereby enhancing the accuracy of CTIS spectral reconstruction using the expectation-maximization (EM) algorithm. This architecture allows us to obtain accurate spectral cubes that match the CTIS diffractive image of real-world scenes, providing a real dataset for training the reconstruction network. A prototype has been built to demonstrate the feasibility of our proposed solution. Furthermore, we also constructed a residual network based on multi-scale and attention mechanism. This network is trained using a combination of simulated and real spectral imaging data. Compared to the reconstruction performance of the EM algorithm and convolutional neural networks, our approach demonstrates superior spectral reconstruction accuracy, validating the importance of real spectral data in CTIS spectral reconstruction tasks.